Answer :
Let's solve the provided problems step by step.
### Problem 1: Time to fall 1,000 feet
Given the formula for the time [tex]\( t \)[/tex] it takes for an object to fall a distance [tex]\( d \)[/tex] feet:
[tex]\[ t = \sqrt{\frac{d}{16}} \][/tex]
We need to find the time it takes for an object to fall 1,000 feet. Substituting [tex]\( d = 1000 \)[/tex] into the formula:
[tex]\[ t = \sqrt{\frac{1000}{16}} \][/tex]
Let's calculate the value inside the square root first:
[tex]\[ \frac{1000}{16} = 62.5 \][/tex]
Now, find the square root of 62.5:
[tex]\[ t = \sqrt{62.5} \approx 7.91 \][/tex]
Rounding this to the nearest whole number, we get:
[tex]\[ t \approx 8 \][/tex]
So, it takes approximately 8 seconds for an object to fall 1,000 feet.
### Problem 2: Distance fallen in 10 seconds
The distance [tex]\( d \)[/tex] an object will fall in [tex]\( t \)[/tex] seconds is modeled by reversing the initial equation:
[tex]\[ d = 16t^2 \][/tex]
We need to find the distance fallen in 10 seconds. Substituting [tex]\( t = 10 \)[/tex] into the formula:
[tex]\[ d = 16 \times (10^2) \][/tex]
[tex]\[ d = 16 \times 100 \][/tex]
[tex]\[ d = 1600 \][/tex]
So, in 10 seconds, an object will fall 1,600 feet.
### Final Statements
1. It takes 8 seconds for an object to fall 1,000 feet.
2. In 10 seconds, an object will fall 1,600 feet.
### Problem 1: Time to fall 1,000 feet
Given the formula for the time [tex]\( t \)[/tex] it takes for an object to fall a distance [tex]\( d \)[/tex] feet:
[tex]\[ t = \sqrt{\frac{d}{16}} \][/tex]
We need to find the time it takes for an object to fall 1,000 feet. Substituting [tex]\( d = 1000 \)[/tex] into the formula:
[tex]\[ t = \sqrt{\frac{1000}{16}} \][/tex]
Let's calculate the value inside the square root first:
[tex]\[ \frac{1000}{16} = 62.5 \][/tex]
Now, find the square root of 62.5:
[tex]\[ t = \sqrt{62.5} \approx 7.91 \][/tex]
Rounding this to the nearest whole number, we get:
[tex]\[ t \approx 8 \][/tex]
So, it takes approximately 8 seconds for an object to fall 1,000 feet.
### Problem 2: Distance fallen in 10 seconds
The distance [tex]\( d \)[/tex] an object will fall in [tex]\( t \)[/tex] seconds is modeled by reversing the initial equation:
[tex]\[ d = 16t^2 \][/tex]
We need to find the distance fallen in 10 seconds. Substituting [tex]\( t = 10 \)[/tex] into the formula:
[tex]\[ d = 16 \times (10^2) \][/tex]
[tex]\[ d = 16 \times 100 \][/tex]
[tex]\[ d = 1600 \][/tex]
So, in 10 seconds, an object will fall 1,600 feet.
### Final Statements
1. It takes 8 seconds for an object to fall 1,000 feet.
2. In 10 seconds, an object will fall 1,600 feet.
